CN104166347A - PD balance control method of underactuation mechanical arm system - Google Patents

Abstract

The invention provides a PD balance control method of an underactuation mechanical arm system. The PD balance control method includes the steps that a controller of the underactuation mechanical arm system sends out a voltage signal, a direct current motor is started and outputs a torque signal to control a master driving arm and an underactuation arm to swing from the vertically downward initial position to the target balance position, an encoder of the master driving arm and an encoder of the underactuation arm are used for detecting the output angle of the master driving arm and the output angle of the underactuation arm respectively in real time, and whether the master driving arm and the underactuation arm deviate from the target balance position or not is judged; if yes, PD balance control is carried out on the underactuation mechanical arm system, and the master driving arm and the underactuation arm are controlled to keep at the target balance position; if not, the current output torque of the direct current motor is kept, and the master driving arm and the underactuation arm are kept at the target balance position. As the controller is used for integration of a control signal and a feedback signal, control over the underactuation mechanical arm is achieved, the response speed is increased, the anti-interference space is enlarged, and stability precision of a swing arm is improved.

Description

A kind of PD balance control method of activation lacking mechanical arm system

Technical field

The invention belongs to automation field, be specifically related to a kind of PD balance control method of activation lacking mechanical arm system.

Background technology

Underactuated Mechanical Systems is extensively present in the fields such as robot for space, aircraft and submarine, is a kind of typical nonholonomic system.Owing to owing actuating arm, can not directly control, general smooth feedback control method is invalid to this type systematic, this type systematic mainly relies on interarticular coupling, the control of actuating arm is owed in realization, therefore general decoupling control method is also invalid to this system, and this makes to owe being controlled to as difficult point of drive system.A large amount of intelligent control algorithms continue to bring out, but it still exists a certain distance apart from actual commercial Application.

It is the controller being most widely used in commercial production that PD controls, it has the advantages such as algorithm is simple, robustness is good, for the control that can set up the deterministic system of mathematical models, be very effective, but be often difficult to obtain good control performance for nonlinear uncertain system.In practical application in industry, conventionally exist the impact of various uncertain factors, the advantage in order to utilize PD to control, generally needs design compensation device to improve the performance of system, but method of estimation in the past does not make full use of the inputoutput data of system, cause data waste.

Summary of the invention

For the problem of prior art existence, the invention provides a kind of PD balance control method of activation lacking mechanical arm system.

Technical scheme of the present invention is:

A PD balance control method for activation lacking mechanical arm system, comprises the following steps:

Step 1: the controller of activation lacking mechanical arm system sends voltage signal, starts direct current generator, direct current generator output dtc signal control main actuating arm and owe actuating arm from initial position pendulum vertically downward to target equilibrium position;

Step 2: detecting in real time respectively the output angle of main actuating arm and the output angle of owing actuating arm with the scrambler of main actuating arm and the scrambler of owing actuating arm, judge main actuating arm and owe the actuating arm equilibrium position that whether departs from objectives, is to perform step 3; Otherwise the output torque that keeps current direct current generator, makes main actuating arm and owes actuating arm to remain on target equilibrium position;

Step 3: activation lacking mechanical arm system is carried out to the control of PD balance, control main actuating arm and owe actuating arm and remain on target equilibrium position;

Step 3.1: according to the kinetic model of activation lacking mechanical arm system, respectively for the dtc signal of direct current generator and the output angle of main actuating arm, the dtc signal of direct current generator and the output angle of owing actuating arm, set up main actuating arm linear model in parallel and owe actuating arm linear model, trying to achieve the output angle of main actuating arm linear model and the output angle of owing actuating arm linear model:

$q_i^{*}(k+1)=(1-A_i\left(z^{-1}\right))q_i(k+1)+B_i\left(z^{-1}\right)u\left(k\right)$

Wherein: i=1,2, i=1 represents main actuating arm, i=2 represents to owe actuating arm; it is the output angle of linear model; q _i(k+1) be the output angle that scrambler detects; The dtc signal that u (k) is direct current generator; A _i(z ^-1), B _i(z ^-1) for characterizing the parameter of activation lacking mechanical arm system dynamics, z ^-1backward shift operator, A _i(z ^-1)=1+a _i1z ^-1+ a _i2z ^-2, B _i(z ^-1)=b _i0+ b _i1z ^-1, a _i1, a _i2, b _i0, b _i1it is unknown parameter;

Step 3.2: the difference of the output angle of the output angle of the main actuating arm that the scrambler of main actuating arm is detected and main actuating arm linear model is dynamic as the virtual not modeling of main actuating arm, owe the output angle of owing actuating arm that the scrambler of actuating arm detects dynamic as the virtual not modeling of owing actuating arm with the difference of output angle of owing actuating arm linear model:

$v_i\left[x\left(k\right)\right]=q_i(k+1)-q_i^{*}(k+1)$

Step 3.3: according to the virtual not modeling of main actuating arm linear model, the dtc signal of owing actuating arm linear model, direct current generator, main actuating arm dynamically and owe the discrete models of the virtual not modeling Dynamic Establishing activation lacking mechanical arm system of actuating arm:

A _i(z ^-1)q _i(k+1)＝B _i(z ^-1)u(k)+v _i[x(k)]

Wherein, q _i(k+1) be the output angle that scrambler detects; v _i[x (k)] is that virtual not modeling is dynamic; The dtc signal that u (k) is direct current generator; I=1,2, i=1 represents main actuating arm, i=2 represents to owe actuating arm; A _i(z ^-1), B _i(z ^-1) for characterizing the parameter of activation lacking mechanical arm system dynamics; By the mechanism model of activation lacking mechanical arm system being carried out to linearization process obtains or empirical value by pid parameter in industrial process oppositely solves and obtains.

Step 3.4: the PD that sets up virtual not modeling dynamic compensation controls model:

H _i(z ^-1)u _i(k)＝R _i(z ^-1)w _i(k)-G _i(z ^-1)q _i(k)-K _i(z ^-1)v _i[x(k-1)]

In formula: H _i(z ^-1), R _i(z ^-1), G _i(z ^-1), K _i(z ^-1) be the PD control model parameter of virtual not modeling dynamic compensation, H _i(z ^-1)=(1+h _iz ^-1), h _iit is undetermined coefficient; R _i(z ^-1)=G _i(z ^-1)=g _i0+ g _i1z ^-1, g _i0=K _pi+ K _di, g _i1=-K _di, K _piand K _discale-up factor and differential coefficient; u _i(k) be the output of the PD control model of virtual not modeling dynamic compensation, the i.e. dtc signal of direct current generator; w _i(k) be current k target equilibrium position constantly; q _i(k) be current k output angle constantly; v _i[x (k-1)] is that k-1 virtual not modeling is constantly dynamic;

Step 3.5: the output angle signal of the main actuating arm detecting according to the scrambler of main actuating arm and owe the output angle signal of owing actuating arm that the scrambler of actuating arm detects, the dtc signal of direct current generator to solve k-1 virtual not modeling constantly dynamic:

$v_i\left[x(k-1)\right]=q_i\left(k\right)-q_i^{*}\left(k\right)$

In formula: $q_i^{*}\left(k\right)=(1-A_i\left(z^{-1}\right))q_i\left(k\right)+B_i\left(z^{-1}\right)u(k-1)$ It is the k output angle of linear model constantly;

Step 3.6: the PD of virtual not modeling dynamic compensation is controlled to the discrete models of model substitution activation lacking mechanical arm system, obtain the closed loop equation of activation lacking mechanical arm system:

[A _i(z ^-1)H _i(z ^-1)+z ^-1B _i(z ^-1)G _i(z ^-1)]q _i(k+1)＝B _i(z ^-1)G _i(z ^-1)w _i(k)+[H _i(z ^-1)-B _i(z ^-1)K _i(z ^-1)]v _i[x(k-1)]+H _i(z ^-1)Δv _i[x(k)]

In formula: Δ v _i[x (k)]=v _i[x (k)]-v _i[x (k-1)], v _i[x (k)] is that current k virtual not modeling is constantly dynamic;

Step 3.7: adopt Assignment of Closed-Loop Poles method to determine that the PD of virtual not modeling dynamic compensation controls model parameter H _i(z ^-1), R _i(z ^-1) and G _i(z ^-1);

Step 3.8: make H _i(z ^-1)-B _i(z ^-1) K _i(z ^-1)=0, makes K _i(1)=H _i(1)/B _i(1) PD that, determines virtual not modeling dynamic compensation controls model parameter K _i(z ^-1);

Step 3.9: control according to the PD of the virtual not modeling dynamic compensation of setting up the output that model obtains the PD control model of virtual not modeling dynamic compensation, and then obtain the dtc signal u (k) of direct current generator:

u(k)＝αu ₁(k)+βu ₂(k)

In formula: α and β are linear weighted function coefficients;

Step 3.10: adjust the output torque of direct current generator according to the dtc signal of the direct current generator obtaining, by main actuating arm with owe actuating arm and be controlled at target equilibrium position.

Beneficial effect:

The present invention be directed to the activation lacking mechanical arm system of single input two outputs, proposed a kind of PD balance control strategy of virtual not modeling dynamic compensation, be intended to solve existing control method and depend on system accurate model, and be difficult to be applied to the defect of industrial process.The topworks of activation lacking mechanical arm system is direct current generator, detects feedback task and generally by impulse type photoelectric encoder, is completed, and by controller, carries out the comprehensive of control signal and feedback signal, realizes the control of activation lacking mechanical arm.Method of the present invention is controlled for the balance of activation lacking mechanical arm, can accelerate the response speed of system, expands anti-interference space, increases substantially the stable state accuracy of swing arm.

Accompanying drawing explanation

Fig. 1 is that the PD of virtual not modeling dynamic compensation of the activation lacking mechanical arm system of the specific embodiment of the invention controls model control strategy block diagram;

Fig. 2 is the activation lacking mechanical arm Pendubot system architecture schematic diagram of the specific embodiment of the invention;

Fig. 3 is the LQR contrast experiment's of the specific embodiment of the invention empirical curve;

Fig. 4 is the SDRE contrast experiment's of the specific embodiment of the invention empirical curve;

Fig. 5 is that the PD balance of the specific embodiment of the invention is controlled the empirical curve of (UDCPD);

Fig. 6 is the graph of errors that the PD balance of the specific embodiment of the invention is controlled (UDCPD) main actuating arm;

Fig. 7 is that the PD balance of the specific embodiment of the invention is controlled the graph of errors that (UDCPD) owes actuating arm;

Fig. 8 is the PD balance control method process flow diagram of the activation lacking mechanical arm system of the specific embodiment of the invention;

Fig. 9 be the specific embodiment of the invention activation lacking mechanical arm system is carried out to PD balance control flow chart.

Embodiment

In order to make technical scheme of the present invention and advantage distincter, below in conjunction with drawings and embodiments, the present invention is described in further detail, present embodiment is only for explaining the present invention, but do not limit the present invention.

In present embodiment, the Pendubot inverted pendulum robot experimental system of selecting east, Ningbo large automatic intelligent technology company limited to produce is implemented the PD balance control method of activation lacking mechanical arm system, Adoption Network controller and EasyControl software carry out the realization of control method, this software and Matlab/Simulink seamless link, tap into row method validation by hardware driving interface direct.The control system that the PD balance control method of enforcement activation lacking mechanical arm system adopts mainly comprises PC, Networked controller, direct current generator and 2 VLT12 type high precision photoelectric scramblers.

Fig. 2 is the structural representation of activation lacking mechanical arm Pendubot system, this system by main actuating arm, owe actuating arm and direct current generator forms, be l ₁the length of master arm, l _c1for master arm arrives the distance of barycenter, l with respect to tie point _c2for owing actuating arm, with respect to tie point, arrive the distance of barycenter, q ₁the output angle that represents main actuating arm, q ₂represent the output angle of owing actuating arm.

The PD balance control method of the activation lacking mechanical arm system of present embodiment, as shown in Figure 8, comprises the following steps:

Step 1: the controller of activation lacking mechanical arm system sends voltage signal, starts direct current generator, direct current generator output dtc signal control main actuating arm and owe actuating arm from initial position pendulum vertically downward to target equilibrium position;

Step 2: detecting in real time respectively the output angle of main actuating arm and the output angle of owing actuating arm with the scrambler of main actuating arm and the scrambler of owing actuating arm, judge main actuating arm and owe the actuating arm equilibrium position that whether departs from objectives, is to perform step 3; Otherwise the output torque that keeps current direct current generator, makes main actuating arm and owes actuating arm to remain on target equilibrium position;

Step 3: activation lacking mechanical arm system is carried out to the control of PD balance, control main actuating arm and owe actuating arm and remain on target equilibrium position, as shown in Figure 9;

Step 3.1: according to the kinetic model of activation lacking mechanical arm system, respectively for the dtc signal of direct current generator and the output angle of main actuating arm, the dtc signal of direct current generator and the output angle of owing actuating arm, set up main actuating arm linear model in parallel and owe actuating arm linear model, trying to achieve the output angle of main actuating arm linear model and the output angle of owing actuating arm linear model:

$q_i^{*}(k+1)=(1-A_i\left(z^{-1}\right))q_i(k+1)+B_i\left(z^{-1}\right)u\left(k\right)$

Wherein: i=1,2, i=1 represents main actuating arm, i=2 represents to owe actuating arm; it is the output angle of linear model; q _i(k+1) be the output angle that scrambler detects; The dtc signal that u (k) is direct current generator; A _i(z ^-1), B _i(z ^-1) for characterizing the parameter of activation lacking mechanical arm system dynamics, z ^-1backward shift operator, A _i(z ^-1)=1+a _i1z ^-1+ a _i2z ^-2, B _i(z ^-1)=b _i0+ b _i1z ^-1, a _i1, a _i2, b _i0, b _i1it is unknown parameter;

Choose sampling period T ₀=2ms, by the linearization of activation lacking mechanical arm system dynamics, tries to achieve the parameter of activation lacking mechanical arm system dynamics: A ₁(z ^-1)=1-1.955z ^-1+ 0.999z ^-2, B ₁(z ^-1)=4.4057 * 10 ^-4(1+z ^-1), A ₂(z ^-1)=1-1.955z ^-1+ 0.999z ^-2, B ₂(z ^-1)=-4.4057 * 10 ^-4(1+z ^-1)

Obtain the output angle of main actuating arm linear model and the output angle of owing actuating arm linear model:

$q_1^{*}(k+1)=1.955q_1\left(k\right)-0.999q_1(k-1)+0.0004057u\left(k\right)+0.0004057u(k-1)$

$q_2^{*}(k+1)=1.955q_2\left(k\right)-0.999q_2(k-1)-0.0004057u\left(k\right)-0.0004057u(k-1)$

In formula: q ₁and q (k) ₂(k) be respectively the k output angle and the output angle of owing actuating arm of main actuating arm constantly; q ₁and q (k-1) ₂(k-1) be respectively the k-1 output angle and the output angle of owing actuating arm of main actuating arm constantly; U (k) is the dtc signal of k direct current generator constantly, is unknown; U (k) is the dtc signal of k-1 direct current generator constantly;

Step 3.2: the difference of the output angle of the output angle of the main actuating arm that the scrambler of main actuating arm is detected and main actuating arm linear model is dynamic as the virtual not modeling of main actuating arm, owe the output angle of owing actuating arm that the scrambler of actuating arm detects dynamic as the virtual not modeling of owing actuating arm with the difference of output angle of owing actuating arm linear model:

$v_i\left[x\left(k\right)\right]=q_i(k+1)-q_i^{*}(k+1)$

Wherein: q _i(k+1) be the output angle that scrambler detects; output angle for linear model; I=1,2; I=1 represents main actuating arm, and i=2 represents to owe actuating arm;

Step 3.3: according to the virtual not modeling of main actuating arm linear model, the dtc signal of owing actuating arm linear model, direct current generator, main actuating arm dynamically and owe the discrete models of the virtual not modeling Dynamic Establishing activation lacking mechanical arm system of actuating arm:

A _i(z ^-1)q _i(k+1)＝B _i(z ^-1)u(k)+v _i[x(k)]

Wherein, q _i(k+1) be the output angle that scrambler detects; v _i[x (k)] is that virtual not modeling is dynamic; The dtc signal that u (k) is direct current generator; I=1,2, i=1 represents main actuating arm, i=2 represents to owe actuating arm; A _i(z ^-1), B _i(z ^-1) for characterizing the parameter of activation lacking mechanical arm system dynamics;

Step 3.4: the PD that sets up virtual not modeling dynamic compensation controls model:

H _i(z ^-1)u _i(k)＝R _i(z ^-1)w _i(k)-G _i(z ^-1)q _i(k)-K _i(z ^-1)v _i[x(k-1)]

In formula: H _i(z ^-1), R _i(z ^-1), G _i(z ^-1), K _i(z ^-1) be the PD control model parameter of virtual not modeling dynamic compensation, H _i(z ^-1)=(1+h _iz ^-1), h _iit is undetermined coefficient; R _i(z ^-1)=G _i(z ^-1)=g _i0+ g _i1z ^-1, g _i0=K _pi+ K _di, g _i1=-K _di, K _piand K _discale-up factor and differential coefficient; u _i(k) be the output of the PD control model of virtual not modeling dynamic compensation, the i.e. dtc signal of direct current generator; w _i(k) be current k target equilibrium position constantly; q _i(k) be current k output angle constantly; v _i[x (k-1)] is that k-1 virtual not modeling is constantly dynamic;

Step 3.5: the output angle signal of the main actuating arm detecting according to the scrambler of main actuating arm and owe the output angle signal of owing actuating arm that the scrambler of actuating arm detects, the dtc signal of direct current generator to solve k-1 virtual not modeling constantly dynamic:

$v_i\left[x(k-1)\right]=q_i\left(k\right)-q_i^{*}\left(k\right)$

In formula: $q_i^{*}\left(k\right)=(1-A_i\left(z^{-1}\right))q_i\left(k\right)+B_i\left(z^{-1}\right)u(k-1)$ It is the k output angle of linear model constantly;

$\begin{array}{c}{v}_1\left[x(k-1)\right]=q_1\left(k\right)-q_1^{*}\left(k\right)\\ =q_1\left(k\right)-[1.955q_1(k-1)-0.999q_1(k-2)+0.0004057u(k-1)+0.0004057u(k-2)]\end{array}$

$\begin{array}{c}{v}_2\left[x(k-1)\right]=q_2\left(k\right)-q_2^{*}\left(k\right)\\ =q_2\left(k\right)-[1.955q_2(k-1)-0.999q_2(k-2)-0.0004057u(k-1)-0.0004057u(k-2)]\end{array}$

Step 3.6: the PD of virtual not modeling dynamic compensation is controlled to the discrete models of model substitution activation lacking mechanical arm system, obtain the closed loop equation of activation lacking mechanical arm system:

[A _i(z ^-1)H _i(z ^-1)+z ^-1B _i(z ^-1)G _i(z ^-1)]q _i(k+1)＝B _i(z ^-1)G _i(z ^-1)w _i(k)+[H _i(z ^-1)-B _i(z ^-1)K _i(z ^-1)]v _i[x(k-1)]+H _i(z ^-1)Δv _i[x(k)]

In formula: Δ v _i[x (k)]=v _i[x (k)]-v _i[x (k-1)], v _i[x (k)] is that current k virtual not modeling is constantly dynamic;

Step 3.7: adopt Assignment of Closed-Loop Poles method to determine that the PD of virtual not modeling dynamic compensation controls model parameter H _i(z ^-1), R _i(z ^-1) and G _i(z ^-1);

H ₁(z ^-1)＝1+0.0349z ^-1，R ₁(z ^-1)＝90.4825-86.2491z ^-1，G ₁(z ^-1)＝90.4825-86.2491z ^-1

H ₂(z ^-1)＝1+0.0349z ^-1，R ₂(z ^-1)＝-90.4825+86.2491z ^-1，G ₂(z ^-1)＝-90.4825+86.2491z ^-1

The scale-up factor and the differential coefficient that according to the PD control model parameter of virtual not modeling dynamic compensation, obtain in Fig. 1 are respectively:

K _p1＝4.2334，K _d1＝86.2491，K _p2＝-4.2334，K _d1＝-86.2491

Step 3.8: make H _i(z ^-1)-B _i(z ^-1) K _i(z ^-1)=0, makes K _i(1)=H _i(1)/B _i(1) PD that, determines virtual not modeling dynamic compensation controls model parameter K _i(z ^-1);

The PD that determines virtual not modeling dynamic compensation in Fig. 1 controls model parameter K _i(z ^-1):

K ₁(z ^-1)＝1275.4，K ₂(z ^-1)＝-1275.4

Step 3.9: control according to the PD of the virtual not modeling dynamic compensation of setting up the output that model obtains the PD control model of virtual not modeling dynamic compensation, and then obtain the dtc signal u (k) of direct current generator:

u(k)＝αu ₁(k)+βu ₂(k)

In formula: α and β are linear weighted function coefficients;

α＝1，β＝1，

$u_1\left(k\right)=\frac{90.4825w_1\left(k\right)-86.2491w_1(k-1)-90.4825q_1\left(k\right)+86.2491q_1(k-1)-1275.4v_1\left[x(k-1)\right]}{1+0.0349z^{-1}},$

$u_2\left(k\right)=\frac{-90.4825w_2\left(k\right)+86.2491w_2(k-1)+90.4825q_2\left(k\right)-86.2491q_2(k-1)+1275.4v_2\left[x(k-1)\right]}{1+0.0349z^{-1}}$

Wherein, w ₁and w (k) ₁(k-1) be respectively main actuating arm k target equilibrium position and k-1 target equilibrium position constantly constantly, be 90 degree; q ₁and q (k) ₁(k-1) be the main actuating arm k that recorded by scrambler output angle and k-1 output angle constantly constantly; w ₂and w (k) ₂(k-1) be respectively and owe actuating arm k target equilibrium position and k-1 target equilibrium position constantly constantly, be 0 degree; q ₂and q (k) ₂(k-1) be the output angle of owing the actuating arm k moment and the k-1 output angle constantly being recorded by scrambler; v ₁[x (k-1)] and v ₂[x (k-1)] is that k-1 two virtual not modelings are constantly dynamic;

Step 3.10: adjust the output torque of direct current generator according to the dtc signal of the direct current generator obtaining, by main actuating arm with owe actuating arm and be controlled at target equilibrium position.

When the PD balance that records activation lacking mechanical arm system is controlled, main actuating arm and the output angle of owing actuating arm obtain curve as shown in Figure 5.

For assessing validity of the present invention, choose Linear-Quadratic Problem regulator (LQR) and the Riccati equation (SDRE) based on state method as a comparison, compare with the PD balance control method (UDCPD) of the activation lacking mechanical arm system of present embodiment.As shown in Figure 3, the curve of output of SDRE control method as shown in Figure 4 for the curve of output of LQR control method.

The anti-interference space of table 1 activation lacking mechanical arm system

Response time and the steady-state error of table 2 activation lacking mechanical arm system

When table 1 and table 2 have provided LQR, SDRE and UDCPD method and have acted on respectively activation lacking mechanical arm Pendubot system, main actuating arm and owe the experimental result of anti-interference space, response speed and the steady-state error of actuating arm.The steady-state error curve of three kinds of control methods as shown in Figure 6 and Figure 7, has provided respectively main actuating arm and has owed the departure of actuating arm when target equilibrium position.In conjunction with chart, can find out, the PD balance control method of the activation lacking mechanical arm of present embodiment, has expanded the anti-interference space of whole system, the error while having reduced stable state, and the response time of having accelerated system.

Claims (2)

1. a PD balance control method for activation lacking mechanical arm system, is characterized in that: comprise the following steps:

Step 1: the controller of activation lacking mechanical arm system sends voltage signal, starts direct current generator, direct current generator output dtc signal control main actuating arm and owe actuating arm from initial position pendulum vertically downward to target equilibrium position;

Step 2: detecting in real time respectively the output angle of main actuating arm and the output angle of owing actuating arm with the scrambler of main actuating arm and the scrambler of owing actuating arm, judge main actuating arm and owe the actuating arm equilibrium position that whether departs from objectives, is to perform step 3; Otherwise the output torque that keeps current direct current generator, makes main actuating arm and owes actuating arm to remain on target equilibrium position;

Step 3: activation lacking mechanical arm system is carried out to the control of PD balance, control main actuating arm and owe actuating arm and remain on target equilibrium position;

Step 3.1: according to the kinetic model of activation lacking mechanical arm system, respectively for the dtc signal of direct current generator and the output angle of main actuating arm, the dtc signal of direct current generator and the output angle of owing actuating arm, set up main actuating arm linear model in parallel and owe actuating arm linear model, trying to achieve the output angle of main actuating arm linear model and the output angle of owing actuating arm linear model:

$q_i^{*}(k+1)=(1-A_i\left(z^{-1}\right))q_i(k+1)+B_i\left(z^{-1}\right)u\left(k\right)$

Wherein: i=1,2, i=1 represents main actuating arm, i=2 represents to owe actuating arm; it is the output angle of linear model; q _i(k+1) be the output angle that scrambler detects; The dtc signal that u (k) is direct current generator; A _i(z ^-1), B _i(z ^-1) for characterizing the parameter of activation lacking mechanical arm system dynamics, z ^-1backward shift operator, A _i(z ^-1)=1+a _i1z ^-1+ a _i2z ^-2, B _i(z ^-1)=b _i0+ b _i1z ^-1, a _i1, a _i2, b _i0, b _i1it is unknown parameter;

Step 3.2: the difference of the output angle of the output angle of the main actuating arm that the scrambler of main actuating arm is detected and main actuating arm linear model is dynamic as the virtual not modeling of main actuating arm, owe the output angle of owing actuating arm that the scrambler of actuating arm detects dynamic as the virtual not modeling of owing actuating arm with the difference of output angle of owing actuating arm linear model:

$v_i\left[x\left(k\right)\right]=q_i(k+1)-q_i^{*}(k+1)$

Step 3.3: according to the virtual not modeling of main actuating arm linear model, the dtc signal of owing actuating arm linear model, direct current generator, main actuating arm dynamically and owe the discrete models of the virtual not modeling Dynamic Establishing activation lacking mechanical arm system of actuating arm:

A _i(z ^-1)q _i(k+1)＝B _i(z ^-1)u(k)+v _i[x(k)]

Wherein, q _i(k+1) be the output angle that scrambler detects; v _i[x (k)] is that virtual not modeling is dynamic; The dtc signal that u (k) is direct current generator; I=1,2, i=1 represents main actuating arm, i=2 represents to owe actuating arm; A _i(z ^-1), B _i(z ^-1) for characterizing the parameter of activation lacking mechanical arm system dynamics;

Step 3.4: the PD that sets up virtual not modeling dynamic compensation controls model:

H _i(z ^-1)u _i(k)＝R _i(z ^-1)w _i(k)-G _i(z ^-1)q _i(k)-K _i(z ^-1)v _i[x(k-1)]

In formula: H _i(z ^-1), R _i(z ^-1), G _i(z ^-1), K _i(z ^-1) be the PD control model parameter of virtual not modeling dynamic compensation, H _i(z ^-1)=(1+h _iz ^-1), h _iit is undetermined coefficient; R _i(z ^-1)=G _i(z ^-1)=g _i0+ g _i1z ^-1, g _i0=K _pi+ K _di, g _i1=-K _di, K _piand K _discale-up factor and differential coefficient; u _i(k) be the output of the PD control model of virtual not modeling dynamic compensation, the i.e. dtc signal of direct current generator; w _i(k) be current k target equilibrium position constantly; q _i(k) be current k output angle constantly; v _i[x (k-1)] is that k-1 virtual not modeling is constantly dynamic;

Step 3.5: the output angle signal of the main actuating arm detecting according to the scrambler of main actuating arm and owe the output angle signal of owing actuating arm that the scrambler of actuating arm detects, the dtc signal of direct current generator to solve k-1 virtual not modeling constantly dynamic:

$v_i\left[x(k-1)\right]=q_i\left(k\right)-q_i^{*}\left(k\right)$

In formula: $q_i^{*}\left(k\right)=(1-A_i\left(z^{-1}\right))q_i\left(k\right)+B_i\left(z^{-1}\right)u(k-1)$ It is the k output angle of linear model constantly;

Step 3.6: the PD of virtual not modeling dynamic compensation is controlled to the discrete models of model substitution activation lacking mechanical arm system, obtain the closed loop equation of activation lacking mechanical arm system:

[A _i(z ^-1)H _i(z ^-1)+z ^-1B _i(z ^-1)G _i(z ^-1)]q _i(k+1)＝B _i(z ^-1)G _i(z ^-1)w _i(k)+[H _i(z ^-1)-B _i(z ^-1)K _i(z ^-1)]v _i[x(k-1)]+H _i(z ^-1)Δv _i[x(k)]

In formula: Δ v _i[x (k)]=v _i[x (k)]-v _i[x (k-1)], v _i[x (k)] is that current k virtual not modeling is constantly dynamic;

Step 3.7: adopt Assignment of Closed-Loop Poles method to determine that the PD of virtual not modeling dynamic compensation controls model parameter H _i(z ^-1), R _i(z ^-1) and G _i(z ^-1);

Step 3.8: make H _i(z ^-1)-B _i(z ^-1) K _i(z ^-1)=0, makes K _i(1)=H _i(1)/B _i(1) PD that, determines virtual not modeling dynamic compensation controls model parameter K _i(z ^-1);

Step 3.9: control according to the PD of the virtual not modeling dynamic compensation of setting up the output that model obtains the PD control model of virtual not modeling dynamic compensation, and then obtain the dtc signal u (k) of direct current generator:

u(k)＝αu ₁(k)+βu ₂(k)

In formula: α and β are linear weighted function coefficients;

Step 3.10: adjust the output torque of direct current generator according to the dtc signal of the direct current generator obtaining, by main actuating arm with owe actuating arm and be controlled at target equilibrium position.

2. the PD balance control method of activation lacking mechanical arm system according to claim 1, is characterized in that: the parameter A of the sign activation lacking mechanical arm system dynamics in the discrete models of the activation lacking mechanical arm system described in step 3.3 _i(z ^-1), B _i(z ^-1) by the mechanism model of activation lacking mechanical arm system being carried out to linearization process obtains or empirical value by pid parameter in industrial process oppositely solves and obtains.